Problem: Simplify the following expression: $z = \dfrac{-63k + 7}{-7k - 49}$ You can assume $k \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-63k + 7 = - (3\cdot3\cdot7 \cdot k) + (7)$ The denominator can be factored: $-7k - 49 = - (7 \cdot k) - (7\cdot7)$ The greatest common factor of all the terms is $7$ Factoring out $7$ gives us: $z = \dfrac{(7)(-9k + 1)}{(7)(-k - 7)}$ Dividing both the numerator and denominator by $7$ gives: $z = \dfrac{-9k + 1}{-k - 7}$